Centralized Radio Access Network (C-RAN) is a new paradigm for wireless networks that centralizes the signal processing in a computing cloud, allowing commodity computational resources to be pooled. While C-RAN improves utilization and efficiency, the computational load occasionally exceeds the available resources, creating a computational outage. This paper provides a mathematical characterization of the computational outage probability for low-density parity check (LDPC) codes, a common class of error-correcting codes. For tractability, a binary erasures channel is assumed. Using the concept of density evolution, the computational demand is determined for a given ensemble of codes as a function of the erasure probability. The analysis reveals a trade-off: aggressively signaling at a high rate stresses the computing pool, while conservatively backing-off the rate can avoid computational outages. Motivated by this trade-off, an effective computationally aware scheduling algorithm is developed that balances demands for high throughput and low outage rates.